Problem: Multiply and simplify the following complex numbers: $({2-i}) \cdot ({-3+2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-i}) \cdot ({-3+2i}) = $ $ ({2} \cdot {-3}) + ({2} \cdot {2i}) + ({-i} \cdot {-3}) + ({-i} \cdot {2i}) $ Then simplify the terms: $ (-6) + (4i) + (3i) + (-2i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (4 + 3)i - 2 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -6 + (4 + 3)i - (-2) $ The result is simplified: $ (-6 + 2) + (7i) = -4+7i $